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What is the next step in finding the inverse of this function?

[tex]\[ y = \frac{x}{6} + 12 \][/tex]


Sagot :

To find the inverse of the function [tex]\( y = \frac{x}{6} + 12 \)[/tex], you should follow these steps:

1. Start with the given function:
[tex]\[ y = \frac{x}{6} + 12 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
This step involves interchanging the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] in the equation to reflect that we are finding the inverse function.
[tex]\[ x = \frac{y}{6} + 12 \][/tex]

3. Solve for [tex]\( y \)[/tex]:
Now, we need to isolate [tex]\( y \)[/tex] on one side of the equation to find the inverse function.

- Subtract 12 from both sides:
[tex]\[ x - 12 = \frac{y}{6} \][/tex]

The next step is:

4. Multiply both sides by 6 to solve for [tex]\( y \)[/tex]:
[tex]\[ 6(x - 12) = y \][/tex]

So, the inverse function is:
[tex]\[ y = 6x - 72 \][/tex]

Therefore, the next step after swapping [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is:
[tex]\[ x - 12 = \frac{y}{6} \][/tex]